Reusing Animations for another character?
Yes, but you have to make sure that the objects (rigs) are identical.

The Action Editor

Either open up a Dope Sheet window or change to the Animation Screen layout.



Change to the Action Editor in the dropdown menu where it likely currently says Dope Sheet.

 --> 

If you select the rig that you already have animated, it will probably display something like ArmatureAction where it says + New in the above screenshot. If you select the unanimated armature, you can select ArmatureAction from the dropdown menu to the left of + New.

The Process:



This can work for any number and any type of object. For example, if I have a cube keyframed for X-Location and X-Rotation, I can use the same method to copy its movements to a nearby cone and cylinder.

Extended uses:



The demo .blend:



Hope this helps; feel free to ask questions!